{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Filters  <img src='data/images/logo.png' width=50 align='left'> \n",
    "\n",
    "author: Thomas Haslwanter \\\n",
    "date: June-2020"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standard packages\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "\n",
    "# Special imports\n",
    "from scipy.io.wavfile import read\n",
    "from IPython.display import Audio, display\n",
    "from scipy import signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#curDir = r'C:\\Users\\p20529\\Coding\\Python\\th\\CSS\\ipynb'\n",
    "audioDir = r'data\\sounds'\n",
    "#os.chdir(curDir)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two groups of linear filters:\n",
    "\n",
    "* *Finite Impulse Response (FIR)*-filters\n",
    "* *Infinite Impulse Response (IIR)*-filters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample data\n",
    "\n",
    "We will use the following data to demonstrate the effect of linear filters on these input data:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Noisy Sine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate a noisy sine-wave\n",
    "rate = 10 # [Hz]\n",
    "dt = 1/rate\n",
    "t = np.arange(0, 20, dt)\n",
    "(amp, noise_amp) = (5, 1)\n",
    "x = amp * np.sin(t) + noise_amp *np.random.randn(len(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "rate = 500\n",
    "t = np.arange(0,1,1/rate)\n",
    "freqs = [3, 50]\n",
    "amps = [2, 0.5]\n",
    "x = np.zeros(t.shape)\n",
    "for freq, amp in zip(freqs,amps):\n",
    "    x += amp * np.sin(2*np.pi*freq*t)\n",
    "    \n",
    "plt.plot(t,x)\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Signal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Impulse and Step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Step')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Definition of *Impulse*\n",
    "impulse = np.zeros(50)\n",
    "impulse[10] = 1\n",
    "\n",
    "# Definition of *Step*\n",
    "step = np.zeros(50)\n",
    "step[10:] = 1\n",
    "\n",
    "# Show impulse and step\n",
    "fig, axs = plt.subplots(1,2)\n",
    "axs[0].plot(impulse)\n",
    "axs[0].set_title('Impulse')\n",
    "\n",
    "axs[1].plot(step)\n",
    "axs[1].set_title('Step')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finite Impulse Response-Filters (FIR)\n",
    "\n",
    "FIR-filters are essentially weighted moving-average filters:\n",
    "\n",
    "<img src='data/images/MovingFilter.jpg' width=500>\n",
    "\n",
    "Note the following aspects of FIR-filters:\n",
    "\n",
    "* the input *feeds forward* to the output (i.e. there is no feedback)\n",
    "* compared to the input, the output is delayed\n",
    "* an *impulse* in the input (i.e. an input where $x_i=1$, and all other x's are 0) has only a finite effect on the output.\n",
    "\n",
    "FIR-filters are amazingly versatile, and can be used to smooth and differentiate data. For example, if you have not yet come in contact with *Savitzky-Golay*-filters, check them out: it is may favorite filter, and can be used to simultaneously smooth the data, and calculate an arbitrary derivative."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Averaging Filter (\"Running Mean\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "win_length = 11\n",
    "\n",
    "# Filter coefficients\n",
    "a = 1              # for FIR-filters, \"a\" is always \"1\"\n",
    "b = np.ones(win_length)/win_length    # the weight-coefficients\n",
    "\n",
    "averaged = signal.lfilter(b, a, x) # apply the filter to the input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x26ad5fa44f0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show the raw-data and the averaged signal\n",
    "plt.plot(t, x, label='raw')\n",
    "plt.plot(t, averaged, label='averaged')\n",
    "plt.xlabel('Time [s]')\n",
    "plt.ylabel('Position [m]')    # We interpret the data here as \"position\"-data\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Impulse Response\n",
    "\n",
    "**Important:** The impulse response of an FIR-filter is equal to the filter coefficients!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x26ad6020460>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "impFiltered = signal.lfilter(b,a, impulse)\n",
    "\n",
    "plt.plot(impulse)\n",
    "plt.plot(impFiltered, 'r*')\n",
    "plt.legend(['Input', 'Output'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While an averaging filter does reduce the noise, it also induces a time-delay in the filtered signal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Differentiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "b_2pnt_diff = np.r_[1, -1]/dt\n",
    "diff_2pnt = signal.lfilter(b_2pnt_diff, a, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Velocity [m/s]')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, diff_2pnt)\n",
    "plt.xlabel('Time [s]')\n",
    "plt.ylabel('Velocity [m/s]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, not so useful :(\n",
    "\n",
    "Here a *Savitzky-Golay* filter comes in handy, which allows us to smooth and differentiate the data in one go"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Savitzky-Golay Filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "diff_savgol = signal.savgol_filter(x, window_length=21, polyorder=3, deriv=1, delta=dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Velocity [m/s]')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, diff_savgol)\n",
    "plt.xlabel('Time [s]')\n",
    "plt.ylabel('Velocity [m/s]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's a lot better! What you have to watch out for: at the beginning and at the end of every linear filter, one has to allow for transient artefacts!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another advantage of Savitzky-Golay filters: they are much better at reproducing maxima and minima:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'zoomed in')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.arange(-20, 21)\n",
    "x = t**2\n",
    "\n",
    "averaged = signal.lfilter(b, 1, x)\n",
    "sg_filtered = signal.savgol_filter(x, window_length=win_length, polyorder=3, deriv=0)\n",
    "\n",
    "fig, axs = plt.subplots(1,2)\n",
    "axs[0].plot(t, x, '-*', label='raw')\n",
    "axs[0].plot(t, averaged, label='averaged')\n",
    "axs[0].plot(t, sg_filtered, label='SavGol')\n",
    "axs[0].legend()\n",
    "\n",
    "axs[1].plot(t,x, '-*', label='raw')\n",
    "axs[1].plot(t, averaged, label='averaged')\n",
    "axs[1].plot(t, sg_filtered, label='SavGol')\n",
    "axs[1].set_xlim([-10, 10])\n",
    "axs[1].set_ylim([0, 50])\n",
    "axs[1].set_title('zoomed in')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[4_DataDisplay](4_DataDisplay.ipynb)<img src=\"data\\images\\Forward_Backward.png\" align='middle'>[5_IIR_Filters](5_IIR_Filters.ipynb)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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